TY - GEN

T1 - On stability analysis with the v-gap metric and integral quadratic constraints

AU - Khong, Sei Zhen

AU - Cantoni, Michael

PY - 2011/12/1

Y1 - 2011/12/1

N2 - This is part of an effort to extend Vinnicombe's v-gap metric based analysis of uncertain feedback interconnections to a linear time-varying setting. The first results involved using integral quadratic constraints (IQCs) to characterise the uncertainty and the existence of v-gap homotopies. Recent work establishes more familiar results in terms of v-gap balls, via the properties of graph symbols and generalised Wiener-Hopf and Hankel operators revealed by the initial work. In this paper, the additional flexibility of IQC based analysis is reconciled with a v-gap ball based stability result. That is to say, we show the latter can be recovered within the original IQC and v-gap homotopy based framework. To this end, path-connectedness of v-gap balls plays a central role. This is established by exploiting a linear fractional characterisation of the v-gap metric and the existence of a certain J-spectral factorisation, which is shown to be the case for finite-dimensional systems with stabilisable and detectable state-space realisation.

AB - This is part of an effort to extend Vinnicombe's v-gap metric based analysis of uncertain feedback interconnections to a linear time-varying setting. The first results involved using integral quadratic constraints (IQCs) to characterise the uncertainty and the existence of v-gap homotopies. Recent work establishes more familiar results in terms of v-gap balls, via the properties of graph symbols and generalised Wiener-Hopf and Hankel operators revealed by the initial work. In this paper, the additional flexibility of IQC based analysis is reconciled with a v-gap ball based stability result. That is to say, we show the latter can be recovered within the original IQC and v-gap homotopy based framework. To this end, path-connectedness of v-gap balls plays a central role. This is established by exploiting a linear fractional characterisation of the v-gap metric and the existence of a certain J-spectral factorisation, which is shown to be the case for finite-dimensional systems with stabilisable and detectable state-space realisation.

KW - Feedback

KW - integral quadratic constraints

KW - linear fractional transformations

KW - path-connectedness

KW - time-varying systems

KW - v-gap metric

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M3 - Conference contribution

AN - SCOPUS:84856111908

SN - 9780858259874

T3 - Proceedings of the 2011 Australian Control Conference, AUCC 2011

SP - 519

EP - 524

BT - Proceedings of the 2011 Australian Control Conference, AUCC 2011

T2 - 1st Australian Control Conference, AUCC 2011

Y2 - 10 November 2011 through 11 November 2011

ER -